Arctan free online calculator

Online arctan(x) calculator. Inverse tangent calculator.

°
rad

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Arctangent definition

The arctangent of x is defined as the inverse tangent function of x when x is real (x∈ℝ).

When the tangent of y is equal to x:

tan y = x

Then the arctangent of x is equal to the inverse tangent function of x, which is equal to y:

arctan x= tan-1 x = y

Example

arctan 1 = tan-1 1 = π/4 rad = 45°

Graph of arctan

Arctan rules

Rule nameRule
Tangent of arctangent

tan( arctan x ) = x

Arctan of negative argument

arctan(-x) = - arctan x

Arctan sum

arctan α + arctan β = arctan [(α+β) / (1-αβ)]

Arctan difference

arctan α - arctan β = arctan [(α-β) / (1+αβ)]

Sine of arctangent

Cosine of arctangent

Reciprocal argument
Arctan from arcsin
Derivative of arctan
Indefinite integral of arctan

Arctan table

xarctan(x)

(rad)

arctan(x)

(°)

-∞-π/2-90°
-3-1.2490-71.565°
-2-1.1071-63.435°
-√3-π/3-60°
-1-π/4-45°
-1/√3-π/6-30°
-0.5-0.4636-26.565°
00
0.50.463626.565°
1/√3π/630°
1π/445°
3π/360°
21.107163.435°
31.249071.565°
π/290°

Arctan on calculator

In order to calculate arctan(y) on a calculator:

  1. Press shift+tan buttons.
  2. Enter the angle.
  3. Press the Calculate button.

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